Answer
$$3$$
Work Step by Step
$$\eqalign{
& \int_1^4 {\frac{4}{{{x^2}}}} dx \cr
& {\text{negative exponent}} \cr
& = \int_1^4 {4{x^{ - 2}}} dx \cr
& {\text{find the antiderivative by the power rule}} \cr
& = \left( {\frac{{4{x^{ - 1}}}}{{ - 1}}} \right)_1^4 \cr
& = - 4\left( {\frac{1}{x}} \right)_1^4 \cr
& {\text{part 1 of fundamental theorem of calculus}} \cr
& = - 4\left( {\frac{1}{4} - \frac{1}{1}} \right) \cr
& {\text{simplify}} \cr
& = - 4\left( { - \frac{3}{4}} \right) \cr
& = 3 \cr} $$
